Graphs and functions Quiz 1

Question 1

Determine $$(f\,o\,f)\,(x)$$ for the function $$f(x) = \dfrac{3}{{2 + x}},x 
e  - 2$$.

Accepted Answer

$$\dfrac{{3x + 6}}{{2x + 7}}$$

Answer

$$\dfrac{{6x + 3}}{{4x + 5}}$$

Answer

$$\dfrac{{2x + 5}}{{5x + 3}}$$

Answer

$$\dfrac{{4x + 7}}{{7x + 2}}$$

Question 2

Determine $$f(x) + f\left( {\dfrac{1}{{ - 2x}}} \right)$$ if $$f\left( x \right) = 24x - 29$$.

Accepted Answer

$$\dfrac{{48{x^2} - 58x - 12}}{x}$$

Answer

$$\dfrac{{48{x^2} + 58x + 12}}{x}$$

Answer

$$\dfrac{{48{x^2} - 58x + 12}}{x}$$

Answer

$$\dfrac{{48{x^2} + 58x - 12}}{x}$$

Question 3

Choose the correct option which indicates the vertex and the graph of the function $$f(x)\, = \, - 2{x^2}$$.

Accepted Answer

$$\left( {0,0} ight) \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/782ef1d3-53f5-44bc-870f-1c6ec6c82b562380656394973499107.png"/>

Answer

$$\left( {1,1} ight) \ $$  <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/bcf88f64-7d7c-40df-a19c-f53c63f0ff155402765894239652148.png"/>

Answer

$$\left( {2,2} ight) \ $$  <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/99222823-fdb5-4728-bf78-ada9ba92d8624369832769473783767.png"/>

Answer

$$\left( {3,3} ight) \ $$ <img  src="https://cmds-vedantu.s3.ap-southeast-1.amazonaws.com/prod/question-sets/4925948f-227c-4846-8274-948b527a12ab1714357167104597853.png"/>

Question 4

The domain of $$\sqrt {7x - 3} $$ is:

Accepted Answer

$$\left[ {\dfrac{3}{7},\infty } \right)$$

Answer

$$\left[ { - \dfrac{3}{7},\infty } \right)$$

Answer

$$\left( { - \infty ,\dfrac{3}{7}} \right]$$

Answer

$$\left( {\dfrac{3}{7},\infty } \right)$$

Question 5

If $${f_q}\left( x \right) = \dfrac{1}{2}\left( {{{\sin }^q}x + {{\cos }^q}x} \right)$$ where $$x \in R$$ and $$q \geqslant 1$$ , then the value of  $${f_6}\left( x \right) + {f_4}\left( x \right)$$ is:

Accepted Answer

$$\dfrac{5}{{12}} - {\sin ^2}x.{\cos ^2}x$$

Answer

$$\dfrac{5}{6} - {\sin ^2}x.{\cos ^2}x$$

Answer

$$\dfrac{5}{{12}} + {\sin ^2}x.{\cos ^2}x$$

Answer

$${\sin ^2}x.{\cos ^2}x - \dfrac{5}{{12}}$$